Desingularization of quiver Grassmannians via Nakajima categories (Q513788)

Quiver Grassmannians are varieties associated to quiver representations of a given dimension vector. They are important object in the context of additive categorification of cluster algebras. In particular, understanding the geometry and topology of such varieties is a problem that has attracted the attention of various authors. In the article under review, the author constructs a desingularization for every quiver Grassmannian associated to a standard self-injective algebra of finite representation type. The main tools used for this purpose are the so-called Nakajima categories (introduced by \textit{B. Keller} and \textit{S. Scherotzke} [J. Reine Angew. Math. 713, 85--127 (2016; Zbl 1401.14091)]), their orbit categories and their standard Frobenius models. Moreover, along the way the author also proves classification theorems about standard Frobenius models of generalized Nakajima categories.